In this Case, Nobody knows precisely if you're online or not; The display word "recently" does a two-way job.. it could mean the user ain't active, it could mean they are...
How about doing...
Last active: Hidden.
Hidden means it is not displayed at all, I don't know the purpose of recently. Are we trying to differentiate someone who is still coming online like BlackHatCoiner but don't want to display the last seen and someone who hasn't been active for like 355 days and above?